When conventional wisdom refers to 85mm as the perfect lens for portraits, it refers to 85mm for a full frame sensor. Is this right? In that case, is it correct to apply the crop factor and say a 55mm F1.8 would be a perfect lens for portraits on an APS-C?

2 Answers
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In terms of angle of view a 55mm lens will give the same AoV with a 1.5X APS-C sensor as an 85mm lens on a 36x24mm FF camera.

In terms of exposure you'd need a 55mm f/1.8 to get the same AoV and exposure in the same light as an 85mm f/1.8 on a FF.

In terms of depth of field (DoF), you'd need a 55mm f/1.2 to get the same DoF from the same subject distance as you would get with an 85mm f/1.8 lens on a FF camera. The 55mm f/1.8 on an APS-C camera could only match the DoF of an 85mm lens set at f/2.8 on a FF camera.

Of course opening up the aperture to f/1.2 would change the exposure compared to f/1.8, so you'd either need to change the shutter time or the ISO to compensate.